The new Microsoft Authenticator will combine different pieces of Microsoft's current set of authenticator apps into a new single app that will work with both Microsoft accounts and Azure Active Directory accounts. The new app is meant for both consumer and enterprise customers.
The coming app will allow users to simply click an "approve" button in a notification to complete their two-factor authentications. The coming app will support wearables including Apple Watch and Samsung Gear, and will support fingerprint-based approvals instead of passcodes on iPhones and Android phones. (I'm asking about support for Microsoft Band and Windows Phones, since Microsoft's post on this mentions neither.)
Update: Good news for Band and WP fans. This just in from a spokesperson: "The Windows Phone app will ship along with iOS and Android -- it's a Universal app. MS Band is on the roadmap, but not supported in the first release. Microsoft is still working through the final support matrix."
A bit more: In case it wasn't clear, it's Windows Phones running Windows 10 Mobile that will be supported by the new Authenticator. The app is designed for mobile devices, not PCs or laptops. "Microsoft Authenticator will not support Windows Hello unlock in the first release, but this is on the priority list for future updates and Microsoft has publicly demoed working prototypes already," the spokesperson added.
Enterprise users will have the ability to sign in through certificates instead of passwords, according to Microsoft's July 25 blog post announcing availability of the coming app.